Transum Software

Exam-Style Question on Statistics

A mathematics exam-style question with a worked solution that can be revealed gradually

List Of Questions Exam-Style Question More Statistics Questions More on this Topic

Question id: 715. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

(a) The list shows 18 temperatures, in degrees Celsius, at 2pm on different days in Honeyville.

19 23 23 16 22 18 29 18 23
24 16 23 20 25 23 27 27 23

(i) Construct a stem-and-leaf diagram to show this information.

(ii) Find the median.

(iii) Find the lower quartile.

(iv) Graham draws a pie chart to show this information.

Calculate the sector angle for the number of days the temperature is 23°C.

(b) The box-and-whisker plot shows information about the masses, in grams, of some stones.

Box Plot

(i) Find the median.

(ii) Find the range.

(iii) Find the interquartile range.

(c) (i) The time, \( t \) minutes, spent exercising in one week by each of 184 students is recorded. The table shows the results.

$$ \begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 60 & 5 \\ 60 < t \leq 80 & 12 \\ 80 < t \leq 90 & 55 \\ 90 < t \leq 100 & 90 \\ 100 < t \leq 150 & 22 \\ \hline \end{array} $$

Calculate an estimate of the mean.

(ii) A new table with different class intervals is completed.

$$ \begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 90 & 72 \\ 90 < t \leq 150 & 112 \\ \hline \end{array} $$

On a histogram the height of the bar for the \( 40 < t \leq 90 \) interval is 7.2 cm.

Calculate the height of the bar for the \( 90 < t \leq 150 \) interval.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.

Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.

This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.

A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.



Drag this panel down to reveal the solution

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


Exam-Style Questions Main Page


Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.


Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2024 WWW.TRANSUM.ORG

©1997 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to